Get post ID of next post by date?

Hi, I’m trying to make an “Other Posts” section in my sidebar on my single.php page where I’d like to have links to the next and previous post entries (and maybe even the next next and previous previous). I’m not interested in the next_post_link() function because it is too specific, and I’d like to pull other information from each post like an attached image, etc. Is there any way I can get get the ID of the next and previous chronological post ID in the same category?

Maybe there is a plugin that handles this. It would be even better to find something that can tell if it’s the first or last post so I don’t need to code that too. If I do have to code it, does anybody know how to evaluate if a post is the earliest or latest post in it’s category?

Thanks so much, I appreciate the help.
David